{% extends 'homepage.html' %}
{% block content %}

<p>The database consists of fields from three sources:
<ol>
<li>The PARI database from the Bordeaux PARI group
<li>Additional totally real fields of degrees from 6 to 10 computed by
  John Voight.
<li>Additional fields from John Jones's database (work in progress).
</ol>
</p>

<h3>Details of the fields contained in the database</h3>
<p>
<ol>
<li>PARI database discriminant ranges.  It is possible that the
  discriminant range depends further on the signature, but this is not
  shown here.
<p>
<table>
{% set row_class = cycler("odd", "even") %}
<tr>
<th>degree</th>
<th>minimum discriminant</th>
<th>maximum discriminant</th>
</tr>
<tr class="{{ row_class.next() }}"><td>1<td>\(1\)<td>\(1\)</tr>
<tr class="{{ row_class.next() }}"><td>2<td>\(-10^6\)<td>\(10^6\)</tr>
<tr class="{{ row_class.next() }}"><td>3<td>\(-10^6\)<td>\(2\cdot10^6\)</tr>
<tr class="{{ row_class.next() }}"><td>4<td>\(-10^6\)<td>\(10^6\)</tr>
<tr class="{{ row_class.next() }}"><td>5<td>\(-10^6\)<td>\(2\cdot10^7\)</tr>
<tr class="{{ row_class.next() }}"><td>6<td>\(-10^6\)<td>\(10^7\)</tr>
<tr class="{{ row_class.next() }}"><td>7<td>\(-11841551\)<td>\(149324209\)</tr>
</table>
</p>
<li>Voight database additional discriminant ranges.  For degrees up to
  9, the database contains all totally real fields with discriminant
  in the given range.
<p>
<table>
{% set row_class = cycler("odd", "even") %}
<tr>
<th>degree</th>
<th>minimum discriminant</th>
<th>maximum discriminant</th>
</tr>
<tr class="{{ row_class.next() }}"><td>6<td>\(1\)<td>\(16771805\)</tr>
<tr class="{{ row_class.next() }}"><td>7<td>\(1\)<td>\(213873729\)</tr>
<tr class="{{ row_class.next() }}"><td>8<td>\(1\)<td>\(2556640000\)</tr>
<tr class="{{ row_class.next() }}"><td>9<td>\(1\)<td>\(25405254289\)</tr>
<tr class="{{ row_class.next() }}"><td>10<td>\(1\)<td>\(7623696325213\)</tr>
</table>
</p>
<li>Jones database additional fields (work in progress).
</ol>
</p>

{% endblock %}
</html>
